The distribution pattern of squares on the stability of F 4F 6-(BN) n ( n = 10–22) polyhedrons

Abstract

To gain an insight into the structures and stability of F 4F 6-(BN) n polyhedrons with alternation of B and N atoms, a density functional theory study was performed on all isomers of F 4F 6-(BN) n polyhedrons with n between 10 and 22. The calculation results demonstrate that the lowest energy isomers do not contain B 44 bonds (the bonds shared by two squares) and the energies of those isomers containing B 44 bonds increase with the number of B 44 bonds linearly, indicating that the energetically favored structures of F 4F 6-(BN) n polyhedrons satisfy the isolated square rule and square adjacency penalty rule. The structural analysis reveals that the stability is determined by the pyramidalization of B and N atoms at the square–square fusion. The binding energy is fitted to the numbers of edges and a model is proposed for predicting the relative stability of these B–N polyhedral molecules.